The deal avoided potential short-term disasters, but it could lead to bigger long-term problems, analysts said.

"This deal is a near-term positive for the market as key fiscal deadlines could shift, but the debt ceiling punt was more of a shank and our sense is that it may materially complicate the GOP's legislative agenda," Issac Boltansky and Lukas Davaz, political analysts at the firm Compass Point, said Thursday.

A fractured party

Trump's move to side with Democrats blindsided Republicans. Even McConnell and Ryan were stunned when the president opted against backing up their requests for 18-month, 12-month, and six-month extensions of the debt ceiling. He ultimately sided with Pelosi and Schumer's request for a three-month extension.

While McConnell and Ryan attempted to sell their members on the deal, a sizeable minority of Republican lawmakers in both the House and Senate ended up vote against the package. Some of them vented their frustrations in the open.

The deal also created another wedge between Trump and the leaders of his own party, with whom he has feuded consistently over the first seven-plus months of his presidency.

"It doesn't help our leadership to try to hold us Republicans together on anything when they know the president will chop them off at the knees," a House GOP member close to Ryan told Politico. "Trump has got to start caring more about his colleagues over here."

Some members in the House are questioning whether Ryan should continue as House speaker. Ryan publicly bashed the three-month debt ceiling suspension as "ridiculous" hours before Trump cut the deal in front of him.

For Schumer and Pelosi, the deal was a coup that strengthens their hand in negotiations to come, said Chris Krueger, an analyst at Cowen Washington Research Group.

"Keep telling yourself that Congress can walk and chew gum at the same time if you want, but the reality is that from now until December 15 the newly-created fiscal cliff is going to take the oxygen out of everything — most specifically tax reform," Krueger wrote on Thursday in a note to clients. "And Democrats will have even more leverage after Trump managed to agree to a policy punt minutes after his House quarterback labeled it a terrible play."

With a new fiscal cliff and a better relationship with Trump, Schumer and Pelosi could score some political victories, said Greg Valliere, chief strategist at Horizon Investments.

"We thought Chuck Schumer was in the witness protection program this summer, virtually absent from the fray - but now he and Nancy Pelosi have a seat at the table," Valliere said in a note Thursday. "Trump might understand real estate deals, but he's a rube when it comes to dealing with Congress. The Democrats want more spending, no tax cuts for the rich, and protection for the 'Dreamers' - and those goals now look attainable in a mega-deal this winter."

Some Republicans admitted that Schumer and Pelosi were able to come out on top and place themselves in a strong negotiating position.

"I think that they would be accurate in suggesting that Democrats had a win on this because there are no structural reforms to debt ceiling that was included with the debt ceiling vote," Rep. Mark Meadows, chair of the conservative Freedom Caucus, said Friday.

A tougher tax road

The deal could also bring negative setbacks for the GOP's push to reform the nation's tax code.

The White House argued the deal would "clear the deck" for tax reform, but it likely makes the pile of issues in December an even bigger impediment to passing a major piece of legislation.

"By delaying huge budget issues until a new December 8 deadline, proponents of a tax bill will get a little time this fall to at least come up with a legislative text," Valliere wrote in a note to clients Thursday. "But the idea of enacting a tax cut by year-end, always far-fetched, is dead."

Mick Mulvaney, Donald Trump, and Steven Mnuchin
Pool/Getty Images

Trump's most important negotiators on the tax reform effort now find themselves in poor position.Trump's other guru on the tax push, Gary Cohn, is on Trump's bad side, and his influence in the process is in question.

Meanwhile, House GOP members booed and hissed at Office of Management and Budget director Mick Mulvaney and Treasury Secretary Steven Mnuchin during a meeting before a vote on the package Friday. Trump's deal also visibly destabilizes Mnuchin's influence, Valliere said.

"The President's point man, Steve Mnuchin, was humiliated yesterday - cut off by Trump virtually in mid-sentence; how can Mnuchin credibly deal with Republicans on a complex tax bill when they know he might get undercut at any moment?" Valliere wrote.